Supplementary Information for
Position-specific and Clumped Stable Isotope Studies: Comparison of the
Urey and Path-Integral Approaches for Carbon Dioxide, Nitrous Oxide,
Methane, and Propane
Michael A. Webb and Thomas F. Miller III
∗
Department of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125
E-mail: tfm@caltech.edu
Contents
PIMC Partition function ratios and equilibrium constants . . . . . . . . . . . . . . . . . S-2
Normal mode wave numbers for CO
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . S-3
Normal mode wave numbers for N
2
O . . . . . . . . . . . . . . . . . . . . . . . . . . . S-4
Normal mode wave numbers for methane. . . . . . . . . . . . . . . . . . . . . . . . . . S-5
Zero-point energies for Urey-AHO calculations . . . . . . . . . . . . . . . . . . . . . . S-6
*
To whom correspondence should be addressed
S-1
Table S - 1:
Partition function ratios and equilibrium constants calculated using PIMC. Statistical errors
are in parentheses and apply to the last digit.
T (K)
∆
16
O
13
C
18
O
-HB
∆
16
O
13
C
18
O
-LB
R
16
O
12
→
13
C
16
O
R
16
O
12
→
13
C
18
O
K
R
16
O
12
→
13
C
16
O
R
16
O
12
→
13
C
18
O
K
300
1
.
34246
(
8
)
1
.
34374
(
7
)
0
.
99904
(
8
)
1
.
340520
(
9
)
1
.
341808
(
9
)
0
.
999040
(
9
)
400
1
.
26788
(
3
)
1
.
26861
(
5
)
0
.
99942
(
5
)
1
.
26634
(
1
)
1
.
267067
(
9
)
0
.
99943
(
1
)
500
1
.
22730
(
2
)
1
.
22774
(
5
)
0
.
99964
(
4
)
1
.
225898
(
6
)
1
.
226335
(
6
)
0
.
999643
(
7
)
600
1
.
20224
(
6
)
1
.
20254
(
3
)
0
.
99975
(
6
)
1
.
201292
(
4
)
1
.
201571
(
3
)
0
.
999768
(
5
)
T (K)
∆
14
N
15
N
16
O
∆
13
CH
3
D
R
14
→
15
N
14
N
16
O
R
14
N
14
→
15
N
16
O
K
R
12
→
13
CH
4
R
12
→
13
CH
3
D
K
300
1
.
25485
(
7
)
1
.
19879
(
8
)
0
.
95533
(
8
)
1
.
25495
(
4
)
1
.
26215
(
5
)
0
.
99429
(
5
)
400
1
.
20456
(
5
)
1
.
16818
(
8
)
0
.
96980
(
8
)
1
.
21374
(
4
)
1
.
21799
(
3
)
0
.
99651
(
4
)
500
1
.
17666
(
6
)
1
.
15091
(
7
)
0
.
97812
(
7
)
1
.
19024
(
1
)
1
.
19297
(
4
)
0
.
99771
(
3
)
600
1
.
15954
(
7
)
1
.
14014
(
7
)
0
.
98327
(
7
)
1
.
17547
(
4
)
1
.
17725
(
3
)
0
.
99849
(
4
)
T (K)
∆
12
CH
3
12
CHD
12
CH
3
∆
12
CH
3
13
CH
2
12
CH
3
R
1
→
2
H
t
R
1
→
2
H
c
K
R
1
→
2
C
t
R
1
→
2
C
c
K
300
32
.
412
(
8
)
29
.
505
(
9
)
0
.
9103
(
4
)
1
.
29398
(
3
)
1
.
27525
(
5
)
0
.
98553
(
4
)
400
14
.
647
(
3
)
13
.
887
(
4
)
0
.
9481
(
3
)
1
.
23400
(
3
)
1
.
22403
(
2
)
0
.
99192
(
3
)
500
9
.
282
(
2
)
8
.
975
(
2
)
0
.
9669
(
2
)
1
.
20158
(
3
)
1
.
19602
(
3
)
0
.
99538
(
3
)
600
6
.
946
(
1
)
6
.
794
(
1
)
0
.
9781
(
2
)
1
.
18212
(
1
)
1
.
17877
(
2
)
0
.
99716
(
2
)
S-2
Table S - 2:
Calculated normal mode wave numbers for CO
2
isotopologues
̄
ω
(cm
−
1
)
16
O
12
C
16
O
16
O
13
C
16
O
16
O
12
C
18
O
16
O
13
C
18
O
̄
̄
ω
1
672
.
8652
653
.
7147
667
.
7360
648
.
4339
̄
ω
2
672
.
8652
653
.
7147
667
.
7360
648
.
4339
̄
ω
3
1353
.
6090
1353
.
6090
1314
.
5261
1314
.
4491
̄
ω
4
2396
.
2675
2328
.
0668
2378
.
4771
2309
.
7949
Calculated from potential energy surface given by Zúñiga et al.,
J. Mol. Spectrosc.
1999
,
195
, 137–146
S-3
Table S - 3:
Calculated normal mode wave numbers for N
2
O isotopologues.
̄
ω
(cm
−
1
)
14
N
14
N
16
O
14
N
15
N
16
O
15
N
14
N
16
O
̄
ω
1
596
.
3070
582
.
6763
592
.
7572
̄
ω
2
596
.
3070
582
.
6763
592
.
7572
̄
ω
3
1298
.
2802
1296
.
4726
1281
.
2784
̄
ω
4
2282
.
1801
2232
.
9808
2259
.
4610
Calculated from potential energy surface given by Zúñiga et al.,
J. Chem. Phys.
1999
,
110
, 6339–6352
S-4
Table S - 4:
Calculated normal mode wave numbers for methane isotopologues.
̄
ω
(cm
−
1
)
12
CH
4
13
CH
4
12
CH
3
D
13
CH
3
D
̄
ω
1
1345
.
3267
1336
.
9620
1188
.
0862
1179
.
9753
̄
ω
2
1345
.
3267
1336
.
9620
1188
.
0862
1179
.
9753
̄
ω
3
1345
.
3267
1336
.
9620
1339
.
8201
1332
.
5799
̄
ω
4
1570
.
3634
1570
.
3634
1508
.
0909
1507
.
0911
̄
ω
5
1570
.
3634
1570
.
3634
1508
.
0909
1507
.
0911
̄
ω
6
3036
.
1496
3036
.
1496
2285
.
1892
2273
.
9839
̄
ω
7
3157
.
0668
3145
.
8475
3071
.
4074
3067
.
7074
̄
ω
8
3157
.
0668
3145
.
8475
3156
.
7900
3145
.
5356
̄
ω
9
3157
.
0668
3145
.
8475
3156
.
7900
3145
.
5356
Calculated from potential energy surface given by Lee et al.,
J. Chem. Phys.
1995
,
102
,
254–261
S-5
Table S - 5:
Zero-point energies (cm
−
1
) for Urey-AHO calculations.
∆
16
O
13
C
18
O
∆
14
N
15
N
16
O
∆
13
CH
3
D
Isotopologue
E
0
Isotopologue
E
0
Isotopologue
E
0
16
O
12
C
16
O
2525
.
394
14
N
14
N
16
O
2370
.
470
12
CH
4
9638
.
564
16
O
13
C
16
O
2472
.
905
14
N
15
N
16
O
2331
.
890
13
CH
4
9610
.
417
16
O
12
C
18
O
2492
.
277
15
N
14
N
16
O
2347
.
310
12
CH
3
D
9032
.
497
16
O
13
C
18
O
2439
.
355
—
—
13
CH
3
D
9002
.
365
S-6